On the Accuracy of the Sine Power Lomax Model for Data Fitting

Abstract

Every day, new data must be analysed as well as possible in all areas of applied science, which requires the development of attractive statistical models, that is to say adapted to the context, easy to use and efficient. In this article, we innovate in this direction by proposing a new statistical model based on the functionalities of the sinusoidal transformation and power Lomax distribution. We thus introduce a new three-parameter survival distribution called sine power Lomax distribution. In a first approach, we present it theoretically and provide some of its significant properties. Then the practicality, utility and flexibility of the sine power Lomax model are demonstrated through a comprehensive simulation study, and the analysis of nine real datasets mainly from medicine and engineering. Based on relevant goodness of fit criteria, it is shown that the sine power Lomax model has a better fit to some of the existing Lomax-like distributions.

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“…Sine power Lomax (SPL) model: Nagarjuna et al 44 introduced a new distribution Sine Power Lomax (SPL) with composition of Sine-G family and Power Lomax distribution by Rady et al 45 The cdf of SPL distribution with the parameters α (shape parameter), β (scale parameter), λ (scale parameter) is given by: From simulation the authors gave a result that on increasing the sample size, the bias and SE of the MLE decreases, also the MMLE converges approximately to the parameter value. For data fitting the proposed model authors use nine real data set against models like Topp Leone Lomax by Oguntunde et al, 46 Power Lomax, Exponentiated Lomax by Cordeiro and Lemonte 47 and Lomax distribution through tests like AIC, CVM, CAIC, BIC, HQIC and found the SPL distribution had the smallest test value and highest value for p value against the rest described models.…”

Review on Distributions Generated Using Trigonometric Functions

“…Subsequently many such families of distributions emerged after the introduction of SS transformation by Kumar, Singh, and Singh (2015). Some among those families and their particular members are discussed in Tomy and Satish (2021) and are as follows: sine square distribution by Al-Faris and Khan (2008), sine generated (Sin-G) family by Kumar et al (2015) and Souza, Junior, De Brito, Chesneau, Ferreira, and Soares (2019a), SS transformed Lindley distribution (SS L (θ) by Kumar, Singh, Singh, and Chaurasia (2018), new exponential with trigonometric function (NET) by Bakouch, Chesneau, and Leao (2018), tan generated (Tan-G) family by Souza, O Júnior, Brito, Chesneau, Fernandes, and Ferreira (2021), cosine generated (Cos-G) family by Souza, Junior, de Brito, Ferreira, Soares et al (2019b), a new family of distributions using cosine-sine (CS) transformation by Chesneau, Bakouch, and Hussain (2018), polyno-expo-trigonometric family by Jamal and Chesneau (2019), sine Topp-Leone generated (STL-G) family by Al-Babtain, Elbatal, Chesneau, and Elgarhy (2020), cosine geometric distribution (CGD) by Chesneau, Bakouch, Hussain, and Para (2020), sinh inverted exponential by Hemeda, Abdallah et al (2020), sin power Lomax (SPL) family by Nagarjuna, Vardhan, and Chesneau (2021), sine Kumaraswamy generated family by Chesneau and Jamal (2021), transformed sin generated (TS-G) family by Jamal, Chesneau, Bouali, and Ul Hassan (2021b). The authors showed that, this approach can be utilised to model a variety of data types, including those related to medicine, engineering, economics, life span, psychiatry, survival etc.…”

The Sine Modified Lindley Distribution

“…The inverse Weibull (IW) distribution proposed by [5] is used as the reference distribution by [4], thus creating the sine IW (SIW) distribution. The sine power Lomax distribution investigated by [6] is one of the most recent works highlighting the importance of the S-G family. It enhances the parental power Lomax distribution on several functional aspects.…”